The Muffin Order
Students at Riverton Primary are baking muffins for a community breakfast and need at least 240 muffins. Two suppliers have sent quotes.
- Baker's Box: packs of 12 muffins at $9.60 each, with 10% off the whole order when 15 or more packs are bought.
- Muffin Mart: packs of 18 muffins at $13.50 each, plus a flat $12.00 delivery fee on every order.
Packs cannot be split, and any muffins left over at the end are given away free. The committee has a budget of $180. The treasurer says cost comes first, but the head of catering would rather not waste food. Mid-week, a local bakery offers to donate 30 muffins, and the committee must decide within the hour whether to change the order they have already planned.
1. Work out the cheapest way to obtain at least 240 muffins. Show the cost of each option and state the saving.
Read the worked answer
Baker's Box
- 240 ÷ 12 = 20 packs exactly.
- Full price: 20 × $9.60 = $192.00
- 20 packs is at least 15, so the 10% discount applies: $192.00 × 0.90 = $172.80
Muffin Mart
- 240 ÷ 18 = 13.33, so 14 packs are needed (13 packs = 234 muffins, which is short).
- 14 × $13.50 = $189.00, then + $12.00 delivery = $201.00
Decision: Baker's Box, 20 packs for $172.80. Saving = $201.00 − $172.80 = $28.20, and it also leaves no spare muffins, so both preferences are satisfied.
2. With the budget of $180, what is the greatest number of muffins the committee can buy? Does the 'no waste' preference change the answer?
Read the worked answer
With the discount, a Baker's Box pack costs $9.60 × 0.90 = $8.64. $180 ÷ $8.64 = 20.83… so only 20 packs can be afforded, because 21 packs would cost 21 × $9.60 × 0.90 = $181.44. 20 packs = 240 muffins for $172.80.
Check Muffin Mart: $180 − $12.00 delivery leaves $168.00; $168.00 ÷ $13.50 = 12.4 → 12 packs = 216 muffins at $174.00.
Greatest number = 240 muffins (Baker's Box). The waste preference is irrelevant here: 240 is exactly the target, so nothing is wasted either way.
3. The donated 30 muffins mean only 210 are now needed. Recalculate the cheapest option and decide whether the planned order should change.
Read the worked answer
Baker's Box (still 18 packs, so the discount still applies)
- 210 ÷ 12 = 17.5 → 18 packs = 216 muffins (17 packs = 204, too few).
- 18 × $9.60 = $172.80; × 0.90 = $155.52
Muffin Mart
- 210 ÷ 18 = 11.67 → 12 packs = 216 muffins.
- 12 × $13.50 = $162.00 + $12.00 = $174.00
Baker's Box is still cheapest, now saving $18.48. The order should drop from 20 packs to 18 packs, freeing up $17.28 and leaving only 6 spare muffins instead of 0 - a trade the committee can accept. Notice that the winning supplier did not change; only the number of packs did.